1. Introduction
Baroclinic waves, or synoptic-scale waves, occur every day in the extratropical troposphere of both hemispheres and cause various weather throughout the midlatitudes (Hoskins and James 2014). Particularly, baroclinic waves with rapidly intensifying cyclones over the sea, the so-called explosive cyclones, or meteorological bombs, pose a serious threat to life and property both far offshore and near shore (Sanders and Gyakum 1980; Roebber 1984; Sanders 1986).
Many prior studies argued that the baroclinic waves play a key role in the formation and maintenance of blocking highs through the interaction between amplified synoptic-scale waves and quasi-stationary planetary-scale waves (Tracton 1990; Tsou and Smith 1990; Higgins and Schubert 1994; Huang and Nakamura 2016; Lupo 1997; Nakamura et al. 1997; Burkhardt and Lupo 2005; Lupo 2021). It is also widely accepted that the growth and maintenance mechanisms of low-frequency atmospheric teleconnections, such as the North Atlantic Oscillation, Pacific–North American pattern, and the western Pacific pattern, involve positive feedback from high-frequency eddy vorticity fluxes (Egger and Schilling 1983; Lau 1988; Dole and Black 1990; Schubert and Park 1991; Branstator 1992; Black and Dole 1993; Ting and Lau 1993; Higgins and Schubert 1994; Feldstein 2002; Orlanski 2003, 2005; Tanaka et al. 2016; Xu et al. 2020; Zhuge and Tan 2021). Blocking high- and low-frequency atmospheric teleconnections influence strongly regional weather/climate anomalies.
In addition, the occurrence of BWP results in simultaneously northward and downward eddy momentum fluxes and northward and upward eddy heat fluxes, which in turn makes an important contribution to the maintenance of the midlatitude eddy-driven jets (Oort 1983; Chang 1993; Hartmann 2007). Very recently, Ma et al. (2021) examined the features of the Lorenz energy cycle for the global atmospheric circulation during the period 1979–2019. They found that the global atmospheric circulation is overall becoming more energetic and efficient and the conversion rates between eddy available potential energy (APE) and eddy kinetic energy (KE) have significantly increased, indicating the strengthening of baroclinic eddy activity in the climate system. They also found that the energy of planetary-scale waves dominates the stationary eddy energy and the energy carried by synoptic-scale waves dominates the transient eddies with a significant increasing trend, which further confirms recent findings on the intensification of eddy activity (Pan et al. 2017) and synoptic-scale waves (Chemke and Ming 2020).
It is, therefore, very important to understand how BWP generates and propagates not only for the understanding of BWP dynamics, but also for the understanding of the formation and maintenance dynamics of the low-frequency teleconnections and atmospheric general circulations. The pioneering studies by Charney (1947) and Eady (1949) indicate that baroclinic instability drives the baroclinic waves. Since then, a large number of studies on the baroclinic waves have been conducted with the normal-mode approach, as in Charney (1947) and Eady (1949). However, the simultaneous growth and decay of baroclinic waves all around the globe, as implicitly implied by the normal-mode approach, is not frequently observed except in the Southern Hemisphere (Randel and Stanford 1985). Rather, some other studies found that baroclinic waves tend to occur in the form of wave packets in both two hemispheres (Chang 1993; Lee and Held 1993; Chang and Yu 1999; Chang 1999, 2005). The wave packets exhibit apparent characteristics of downstream development, with successive perturbations developing toward the downstream side of existing perturbations (Chang 1993; Chang and Orlanski 1993; Orlanski and Katzfey 1991; Orlanski and Chang 1993; Yang et al. 2007). The kinetic energy budget analysis of the wave train over the North Pacific indicates that initially the wave train grows in the more baroclinically unstable region mainly due to baroclinic conversion. As the wave matures, it starts radiating energy downstream via the ageostrophic geopotential fluxes, leading to its demise and the growth of a new wave downstream. In such a way, the storm track is extended from highly unstable regions into relatively stable regions downstream (Chang 1993; Chang and Orlanski 1993). Very recently, some studies found that baroclinic wave activity over the North Pacific not only seeds the North Atlantic storm activity via downstream development on a time scale of days, but also suppresses the North Atlantic storm activity on a time scale of a week and more. The downstream suppression is also apparent for the North Atlantic storm track and Southern Hemisphere storm track (Thompson et al. 2017; Boljka et al. 2021).
The studies of BWP mentioned above have improved our understanding of the mechanisms of propagation and development of BWP. Some issues, however, remain unsolved. For example, Chang (1993) found that barotropic energy conversion serves as an energy source for BWP over the western North Pacific, but it acts as an energy sink over the central and eastern North Pacific. Why does the role of the barotropic energy process vary over the different geographic locations? Also, Chang (1993) found that the zonal ageostrophic geopotential flux plays a key role in the downstream development of BWP, what is the role of the vertical anomalous geopotential flux in the propagation and development of BWP? Furthermore, the roles of the nonlinear processes including feedback forcing by low-frequency eddies and the scale interactions between high- and low-frequency eddies have not been investigated yet. Do they act as an energy source or sink? All the above questions will be examined in this study in view of an energy budget analysis. To this end in this study, day-to-day KE and APE balances for BWP will be performed and the relative contributions of various KE and APE conversion/generation processes will be estimated, for the whole BWP system and its different vertical parts, respectively. In the next section, we will briefly discuss the analysis technique and describe the data used. The main results are represented in section 3, and the summary and discussion will be given in the final section.
2. Data and methods
This study uses daily (0000 UTC) data from the Japanese 55-year Reanalysis (JRA-55) (Ebita et al. 2011; Kobayashi et al. 2015) for winters [November–March (NDJFM)] from 1958 to 2018. Variables used include daily geopotential height, horizontal winds, vertical pressure velocity, air temperature, convective and large-scale condensation heating rate at standard pressure levels, as well as the surface air temperature (SAT). Anomalies for daily variables at each grid point are formed by removing the long-term mean seasonal cycle from the raw data. The long-term mean seasonal cycle is defined as the 60-winter mean value for each calendar day. The data are not filtered in the analyses except when we estimate the relative contributions of high- and low-frequency eddies to KE generation by nonlinear processes of transient eddies and to APE generation by transient eddy heat fluxes, the anomalies are 10-day high- and low-pass filtered (Duchon 1979). The statistical significance of linear regressions is estimated with the Student’s t test (Kosaka et al. 2012).
In the Northern Hemisphere, BWPs differ in their structures and underlying dynamics, depending on their geographic locations (Chang and Yu 1999). In this study, we focus on the BWPs propagating across the Pacific storm track. As in Chang (1993), the BWP pattern here will be defined as the regression of daily geopotential height anomalies against the standardized time series of the unfiltered meridional wind anomalies at the base point (40°N, 180°) at 300 hPa for 1958–2018 winters, which is characterized by a wave train of several main anomaly centers with alternating positive and negative signs over the North Pacific (Fig. 1, day 0). It turns out that the results are not sensitive to the exact choice of position of the base point.
Lag regressions of anomalous 300 hPa unfiltered meridional wind based on time series of 300 hPa unfiltered meridional wind at 40°N, 180° for (top to bottom) lag days [−2, −1, 0, +1, +2]. Red (blue) lines indicate positive (negative) anomalies with contour interval of 2 m s−1 and zero lines are omitted.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
3. Results
a. Structure and evolution of the BWP pattern
We first examine the structure and evolution features of the BWP pattern based on regression analysis using the 300 hPa meridional wind anomalies as the reference time series at the grid (40°N, 180°). Figure 1 gives the lagged-regression maps of the 300 hPa meridional wind anomalies at days −2, −1, 0, +1, and +2. From Fig. 1, we see a wave packet propagating from South Asia into the North Pacific and North America with an apparent feature of downstream development. Initially, at day −2, the wave packet is weak with its anomaly centers located in South and East Asia and the western North Pacific. At day −1, the wave packet intensifies and propagates into the North Pacific. At the same time, the anomaly center over South Asia weakens, and new anomaly centers form over the central east North Pacific. From day −1 to day 0, the wave packet intensifies further and matures, while its upstream side anomalous center over East Asia weakens. Afterward, the wave packet begins to decay, its western anomaly center weakens and a new anomaly center forms again over North America (day +1). At day +2, the wave packet gets weakened again and disappears afterward (not shown). Obviously, the wave packet has a lifespan of 5 days or so.
We now examine the vertical structure of the wave packet, which is illustrated at day 0 as an example. Shown in Fig. 2 are the meridional wind, geopotential, temperature, and vertical velocity anomalies in the longitude–height cross section along 40°N. We see that both the meridional wind and geopotential anomalies have their maxima at the 300 hPa level and show a tilt in phase toward the west with height (Figs. 2a,b), while temperature anomalies show a tilt toward the east with the height (Fig. 2c). The temperature anomalies have their maximum around the 500 hPa level and they reverse sign above the 300 hPa level. The vertical velocity has the maximum also at the 500 hPa level and shows no tilt in phase with height (Fig. 2d). Further inspection of Figs. 2c and 2d indicates that below the 300 hPa level, generally the warm air rises and the cold air sinks, indicating that in the atmosphere below the 300 hPa, there is an energy transfer from APE to KE, which acts as a KE source to drive the wave packet (see below). Above the 300 hPa, the reverse is true: the warm air generally sinks while the cold air rises, which acts as KE sink to damp the wave packet.
Longitude–height plot of regressions for anomalous (a) meridional wind, (b) geopotential height, (c) air temperature, and (d) vertical velocity based on time series of 300 hPa unfiltered meridional wind at 40°N, 180° for lag day 0. Red (blue) lines indicate positive (negative) anomalies with contour interval of 2 m s−1, 20 gpm, 0.5 K, 0.02 Pa s−1 for (a)–(d), respectively, and zero lines are omitted.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
It should be noted that the general features in structure and evolution of the wave packets are in good agreement with the results of Chang (1993) obtained with the European Centre for Medium-Range Weather Forecasts (ECMWF) data for seven winters from 1980 to 1987.
b. Day-to-day KE and APE balances of the BWP pattern
To better understand the mechanisms for the development and propagation of the BWP pattern, we now examine the day-to-day energy balances of the BWP pattern. As we mentioned in the introduction, Chang (1993) has focused on the mechanism of downstream development and examined the roles of several main KE conversion/generation terms in the development and propagation of three main anomaly centers of the wave packets separately. Instead, we here perform the energetics analysis for the BWP pattern as a whole first and then for its different vertical parts and examine both KE and APE budgets. Similar to Tanaka et al. (2016) and Zhuge and Tan (2021), we quantify each of the energy conversion/generation terms relevant to the BWP pattern in Eqs. (1) and (2) based on its regressed anomalies and integrate each term horizontally over the domain (0°–87.5°N, 0°–360°) and vertically from the surface to 100 hPa. The domain integrations of the divergence terms
Figure 3a (Fig. 3d) shows that the APE (KE) tendency matches the sum of the APE (KE) conversion/generation terms quite well. This suggests that the energy budget captures reasonably the essential dynamics of the BWP pattern.
Time series for the APE tendency (solid line) and sum of all the APE conversion/generation terms (dashed line) for the BWP pattern; (b) time series for various APE conversion/generation terms: CPB (blue line), −CKEP (red line), CPE (solid black line), and CPQ (dashed black line); (c) time series for the three components of CPE: CPEH (red line), CPEL (blue line) and CPEHL (black line); (d) as in (a), but for the KE tendency (solid line) and all the APE conversion/generation terms (dashed line) (dashed line); (e) time series for various KE conversion/generation terms: CKEP (red line), CKB (blue line), CKE (solid black line), AGFD (purple line), and CKF (dashed black line); (f) time series for three components of CKE: CKEH (red line), CKEL (blue line) and CKEHL (black line). Units are 1013 kg m2 s−3. The reader is referred to the appendix in Zhuge and Tan (2021) for details of expressions of the energy conversion/generation terms.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Figure 3b indicates that for APE balance the baroclinic energy conversion, CPB (blue line), among the four generation/conversion terms, acts as a dominant APE source throughout the BWP lifespan, with maximum conversion rate occurring at day 0. Most of the APE generated by CPB converts simultaneously into the BWP KE through the APE–KE conversion term (CKEP, red line). Obviously, the CPE term (solid black line) is always negative, which acts as a thermal damping for the BWP pattern. As illustrated in Fig. 3c, high-frequency eddies (red line), low-frequency eddies (blue line), and their interaction (black line) all contribute to the thermal damping. While the diabatic heating, CPQ, also contributes positive APE (Fig. 3b, dashed black line) from day −2 to day +2, with its magnitude being much weaker than the CPB-generated APE.
For KE balance of the BWP pattern (Fig. 3e), the APE–KE conversion, CKEP (red line), which converts APE generated by the baroclinic energy conversion into KE, is always positive and peaks on day 0, acting as a dominant KE source through the whole lifespan of the BWP pattern. Clearly, the barotropic conversion, CKB (Fig. 3e, blue line), contributes positive KE before day −1, and afterward, it contributes considerable negative KE with the peak observed on day 0, acting as a major KE sink to damp the BWP pattern. Similarly, the nonlinear term, CKE (solid black line), contributes positive KE before day 0, and after day 0, it contributes substantial negative KE with the peak observed on day +1, acting also as a major KE sink. The damping effect of CKE is even stronger than that of CKB. Figure 3f further indicates that the nonlinear process associated with high-frequency eddies (red line) contributes positive KE during day −3 to day +1, otherwise, it makes no significant KE contribution. The feedback forcing by low-frequency eddies (blue line) contributes significant negative KE from day −1 to day +3, while the interaction between high- and low-frequency eddies (black line) contributes positive KE before day −1 and substantial negative KE afterward. Both the friction term due to turbulence, CKF (Fig. 3e, dashed black line), and anomalous geopotential flux divergence,
To further understand how the conversion/generation terms in Eqs. (1) and (2) drive the BWP pattern, we now turn to examine in more detail how main conversion/generation terms work. First, we look at the baroclinic energy conversion. Shown in Fig. 4a are the horizontally integrated baroclinic energy conversion (CPB) evaluated at various pressure levels. Clearly, the horizontal integrated baroclinic energy conversion contributes positive APE in the troposphere from the surface to around 250 hPa with maximum conversion occurring at around 400 hPa. In the upper layer from 200 to 100 hPa, the horizontally integrated baroclinic energy conversion contributes to negative APE. As indicated in Fig. 5 (left column), the baroclinic energy conversion at 400 hPa occurs along the climatological East Asia–Pacific jet and the exit of the jet, with positive and negative conversions occurring alternatingly. The APE gain due to the baroclinic energy conversion comes mainly from three positive CPB centers located over East Asia and the western North Pacific at day −2. From day −2 on, these CPB centers displace eastward and intensify rapidly from day −2 through day 0 and then decay sharply (day +1 and day +2). A similar feature of the baroclinic energy conversion is also observed in Chang (1993, see Fig. 12). Figure 5 (center column) indicates that these positive CPB centers are contributed mainly by the second part of CPB,
Time series of horizontally integrated (a) CPB, (b) CKB, (c) CKE (units: 109 m4 s−3) for the BWP pattern at different levels. The integration is calculated over the domain 0°–87.5°N, 0°–360°.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Lag regressions of (left) CPB, (center)
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Lag regressions of the 400 hPa air temperature anomalies (shading) and wind anomalies (arrows) based on time series of 300 hPa unfiltered meridional wind at 40°N, 180° for (top to bottom) lag days [−2, −1, 0, +1, +2]. Red (blue) shading indicates positive (negative) values that are statistically significant at 95% confidence level using the Student’s t test. Scaling for wind anomalies is given at the bottom-right corner for each panel (units: 8 m s−1).
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Further inspection of CKB indicates that among the six parts of the CKB [see Eq. (A17) in Zhuge and Tan 2021], the second part
Time series of
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Lag regressions of (left)
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
One prominent feature in the KE conversions caused by term
Finally, we examine how the nonlinear term works in the KE conversion. Figure 4c indicates that strong CKE occurs in the upper-tropospheric layer from 400 to 200 hPa with maximum conversion occurring at 250 hPa level. As we have seen in Fig. 3e, for earlier days before day 0, CKE contributes positive KE with a peak being observed on day −1. Figure 9 shows that this peak in KE conversion comes mainly from the strong CKE center over the ocean east of Japan, which is contributed by both high-frequency eddies (CKEH) (Fig. 9, second column) and the scale interaction between high- and low-frequency eddies (CKEHL) (Fig. 9, fourth column). On day 0, high-frequency eddies still contribute strong positive KE over the central North Pacific, which is offset by the negative KE caused by the scale interaction between high- and low-frequency eddies. Afterward, the scale interaction dominates the nonlinear processes, which contributes to strong negative KE and damps the BWP pattern heavily (Fig. 9, fourth column). Further examination of every part of CKEHL indicates that it is the advection of high-frequency meridional momentum by low-frequency zonal wind {
Lag regressions of (from left to right) CKE, CKEH, CKEL, and CKEHL at 250 hPa based on the time series of 300 hPa unfiltered meridional wind at 40°N, 180° for (top to bottom) lag days [−2, −1, 0, +1, +2] (shading, 10−4 m2 s−3). Warm (cold) shading indicates positive (negative) values.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
Lagged composites of
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
c. Energetics of the BWP pattern in different vertical layers
It is expected that the BWP pattern dynamics may differ among different atmospheric layers and there exists strong dynamical coupling between different layers. To see this point clearly, we now perform day-to-day energy budget analysis for different pressure layers of the BWP pattern separately. The troposphere is divided into three layers: the lower layer (from the surface to 850 hPa), the middle layer (from 850 to 400 hPa), and the upper layer (from 400 to 100 hPa). The results are not sensitive to the exact choice of the boundaries separating different layers.
For the three tropospheric layers, the KE tendency matches the sum of KE conversion/generation terms well (Figs. 11a–c). This implies that the KE budgets can describe well the essential dynamics of the BWP pattern in the three layers.
Time series of tendency of kinetic energy tendency and the various conversion/generation terms based on the time series of 300 hPa unfiltered meridional wind at 40°N, 180° (units: 1013 kg m2 s−3) in the (a),(d) upper (400–100 hPa), (b),(e) middle (850–400 hPa) and (c),(f) lower (1000–850 hPa) layer of the troposphere.
Citation: Journal of Climate 36, 12; 10.1175/JCLI-D-22-0667.1
In the upper layer (Fig. 11d), the APE–KE conversion and the AGFD term act as major KE sources with AGFD much stronger than the APE–KE conversion. Both CKB and CKE act as major KE sink to damp heavily the BWP pattern all the time except for the early evolution days. CKB and CKE act as KE sources before day −1 and day 0, respectively, and afterward, they act as strong KE sinks to damp the BWP pattern heavily. In the middle layer (Fig. 11e), the APE–KE conversion acts as a dominant KE source, and the AGFD term acts as a dominant KE sink, while the contributions of CKB and CKE are rather weak, compared to the above two terms. In the lower layer (Fig. 11f), in sharp contrast, both the AGFD term and the APE–KE conversion act as KE sources with the former being considerably stronger than the latter, while the turbulent friction term acts as a major damping term, as expected.
The above result indicates that the relative roles of the KE conversion/generation terms in the development and maintenance of the BWP pattern do vary from layer to layer. Particularly, the role of the AGFD term is quite different in the middle layer from the lower and upper layers. It acts as the dominant KE sink in the middle layer, whereas it acts as a dominant KE source in the lower and upper layers. Further inspection of the AGFD term indicates that the contribution of the AGFD term mainly comes from the divergence of the vertical component of anomalous geopotential flux, i.e.,
4. Summary and discussion
Based on the JRA-55 data for winters from 1958 to 2018, we have performed the APE and KE budget analysis for the baroclinic wave packets over the North Pacific. The results indicate that the BWP pattern grows and is maintained by baroclinic instability and decays through barotropic and nonlinear processes.
Strong positive baroclinic energy conversion from the climatological flow into the BWP anomalies takes place in the troposphere below 250 hPa with the peak conversion being observed at 400 hPa through northward (southward) and upward (downward) movements of the warmer (colder) air mass moves northward (southward) and upward (downward) and the APE converts simultaneously into KE for the BWP growth and maintenance through its lifespan. These features are typical characteristics of midlatitude baroclinic waves.
Strong barotropic decay takes place in the upper troposphere from 400 to 200 hPa over the central and eastern North Pacific, where the meridional momentum flux of the BWP pattern is along the meridional gradient of the climatological meridional wind. In this way, there is a KE conversion from the BWP pattern to the background flow, leading to the decay of the BWP pattern. The barotropic decay of the BWP pattern was also observed in Chang (1993) but the mechanism of decay was absent.
The nonlinear decay, which was not explored at all in Chang (1993), also occurs most actively in the upper troposphere over the central and eastern North Pacific. The damping effect of the nonlinear term comes mainly from the scale interaction between high- and low-frequency eddies through the advection of high-frequency meridional momentum by low-frequency zonal wind. This suggests that low-frequency eddies play an active role in decay of the BWP pattern. Note that Lee and Held (1993) and Swanson and Pierrehumbert (1994) once examined the role of nonlinearity in the formation of BWPs developed from a localized disturbance in a zonally uniform and baroclinically unstable flow in numerical experiments. They found that nonlinearity modifies the behavior of the linear wave packet substantially, with the leading edge of the linear wave packet developing into a localized nonlinear wave packet and the trailing end dissipating. Here we further demonstrated that nonlinearity is a main factor for the BWP decay, which is realized through the scale interaction between high- and low-frequency eddies.
It should be pointed out that the divergence term of geopotential fluxes has no net KE contribution to the BWP pattern as a whole though, it actually plays an important role in the dynamical coupling of different parts of the BWP pattern. Orlanski and Katzfey (1991), Orlanski and Chang (1993), Chang and Orlanski (1993), and Chang (1993) once demonstrated that the zonal ageostrophic geopotential flux and its divergence may lead to development of new waves toward the downstream side of existing waves of the BWP pattern. In such a way, the storm track is extended from highly unstable regions into relatively stable regions downstream (Chang 1993). This study, instead, further demonstrated that the BWP pattern persistently radiates anomalous geopotential fluxes vertically from the middle into upper and lower layers of the troposphere, and through this process the energy generated by baroclinic process in the middle layer is transferred simultaneously into the upper and lower layers to drive the BWP anomalies. We, therefore, believe that both the zonal and vertical geopotential fluxes together play an important role in the BWP development and propagation, and in the type-B cyclogenesis (Petterssen and Smebye 1971).
As mentioned in the introduction section, Simmons and Hoskins (1978, 1980) and Randel and Stanford (1985) once studied baroclinic waves in the form of normal modes in zonal symmetry flow with numerical models or a single zonal harmonic dominating the Southern Hemisphere summer flow. Their energetics analysis indicated that the waves grow by baroclinic instability and decay due to the barotropic transfer of energy to the zonal flow, as in the BWP case. How the barotropic decay for waves in a zonally uniform flow works, however, still remains unclear. Also, Simmons and Hoskins (1978) believed that the nonlinearity is important to shape the behavior of the waves. However, their energetics analysis based on the framework of Lorenz (1955) was unable to describe the roles of the nonlinearity neither. To see how the barotropic energy conversion and nonlinearity work, an energetics analysis for individual waves similar to Chang (1993) and the present study is required. These issues become interesting topics for future study.
Recently, Zhuge and Tan (2021) examined the energetics of the western Pacific (WP) pattern of periods of 7–35 days, which is one of the well-known low-frequency wave trains over North Pacific, and found that the baroclinic instability is also an important energy source for growth and maintenance of the WP pattern, as in the BWP case. However, remarkable differences are observed for the two wave packets in roles of the barotropic energy conversion and nonlinearity. The barotropic energy conversion makes only weak KE contribution through the lifespan of the WP pattern, while it acts as a major KE sink for the BWP pattern. The nonlinear term acts as a major KE source for the growth of the WP pattern and a dominant KE sink during the decay stage. In contrast, it makes only weak KE contribution for growth of the BWP pattern and acts as a major KE sink for decay of the BWP pattern. These energetics differences come mainly from the structure differences of the wave packets and their relative positions in the basic flows.
Acknowledgments.
We thank three anonymous reviewers and Dr. Isla Ruth Simpson, editor, very much for their insight comments. This research is supported by National Natural Science Foundation of China (Grants 41375060 and 41875065).
Data availability statement.
The JRA-55 data used in this study were obtained from https://rda.ucar.edu/datasets/ds628.0/. The ERA-Interim data were obtained from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim.
REFERENCES
Black, R. X., and R. M. Dole, 1993: The dynamics of large-scale cyclogenesis over the North Pacific Ocean. J. Atmos. Sci., 50, 421–442, https://doi.org/10.1175/1520-0469(1993)050<0421:TDOLSC>2.0.CO;2.
Boljka, L., D. W. J. Thompson, and Y. Li, 2021: Downstream suppression of baroclinic waves. J. Climate, 34, 919–930, https://doi.org/10.1175/JCLI-D-20-0483.1.
Branstator, G., 1992: The maintenance of low-frequency atmospheric anomalies. J. Atmos. Sci., 49, 1924–1946, https://doi.org/10.1175/1520-0469(1992)049<1924:TMOLFA>2.0.CO;2.
Burkhardt, J. P., and A. R. Lupo, 2005: The planetary- and synoptic-scale interactions in a southeast Pacific blocking episode using PV diagnostics. J. Atmos. Sci., 62, 1901–1916, https://doi.org/10.1175/JAS3440.1.
Chang, E. K. M., 1993: Downstream development of baroclinic waves as inferred from regression analysis. J. Atmos. Sci., 50, 2038–2053, https://doi.org/10.1175/1520-0469(1993)050<2038:DDOBWA>2.0.CO;2.
Chang, E. K. M., 1999: Characteristics of wave packets in the upper troposphere. Part II: Seasonal and hemispheric variations. J. Atmos. Sci., 56, 1729–1747, https://doi.org/10.1175/1520-0469(1999)056<1729:COWPIT>2.0.CO;2.
Chang, E. K. M., 2005: The impact of wave packets propagating across Asia on Pacific cyclone development. Mon. Wea. Rev., 133, 1998–2015, https://doi.org/10.1175/MWR2953.1.
Chang, E. K. M., and I. Orlanski, 1993: On the dynamics of a storm track. J. Atmos. Sci., 50, 999–1015, https://doi.org/10.1175/1520-0469(1993)050<0999:OTDOAS>2.0.CO;2.
Chang, E. K. M., and D. B. Yu, 1999: Characteristics of wave packets in the upper troposphere. Part I: Northern Hemisphere winter. J. Atmos. Sci., 56, 1708–1728, https://doi.org/10.1175/1520-0469(1999)056<1708:COWPIT>2.0.CO;2.
Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor., 4, 136–162, https://doi.org/10.1175/1520-0469(1947)004<0136:TDOLWI>2.0.CO;2.
Chemke, R., and Y. Ming, 2020: Large atmospheric waves will get stronger, while small waves will get weaker by the end of the 21st century. Geophys. Res. Lett., 47, e2020GL090441, https://doi.org/10.1029/2020GL090441.
Dole, R. M., and R. X. Black, 1990: Life cycles of persistent anomalies. Part II: The development of persistent negative height anomalies over the North Pacific Ocean. Mon. Wea. Rev., 118, 824–846, https://doi.org/10.1175/1520-0493(1990)118<0824:LCOPAP>2.0.CO;2.
Duchon, C. E., 1979: Lanczos filtering in one and two dimensions. J. Appl. Meteor., 18, 1016–1022, https://doi.org/10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.
Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1 (3), 33–52, https://doi.org/10.3402/tellusa.v1i3.8507.
Ebita, A., and Coauthors, 2011: The Japanese 55-year Reanalysis “JRA-55”: An interim report. SOLA, 7, 149–152, https://doi.org/10.2151/sola.2011-038.
Egger, J., and H.-D. Schilling, 1983: On the theory of the long-term variability of the atmosphere. J. Atmos. Sci., 40, 1073–1085, https://doi.org/10.1175/1520-0469(1983)040<1073:OTTOTL>2.0.CO;2.
Feldstein, S. B., 2002: Fundamental mechanisms of the growth and decay of the PNA teleconnection pattern. Quart. J. Roy. Meteor. Soc., 128, 775–796, https://doi.org/10.1256/0035900021643683.
Hartmann, D. L., 2007: The atmospheric general circulation and its variability. J. Meteor. Soc. Japan, 85B, 123–143, https://doi.org/10.2151/jmsj.85B.123.
Higgins, R. W., and S. D. Schubert, 1994: Simulated life cycles of persistent anticyclonic anomalies over the North Pacific: Role of synoptic-scale eddies. J. Atmos. Sci., 51, 3238–3260, https://doi.org/10.1175/1520-0469(1994)051<3238:SLCOPA>2.0.CO;2.
Hoskins, B. J., and I. N. James, 2014: Fluid Dynamics of the Midlatitude Atmosphere. John Wiley and Sons, 408 pp.
Huang, C. S. Y., and N. Nakamura, 2016: Local finite-amplitude wave activity as a diagnostic of anomalous weather events. J. Atmos. Sci., 73, 211–229, https://doi.org/10.1175/JAS-D-15-0194.1.
Kobayashi, S., and Coauthors, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 5–48, https://doi.org/10.2151/jmsj.2015-001.
Kosaka, Y., J. S. Chowdary, S.-P. Xie, Y.-M. Min, and J.-Y. Lee, 2012: Limitations of seasonal predictability for summer climate over East Asia and the northwestern Pacific. J. Climate, 25, 7574–7589, https://doi.org/10.1175/JCLI-D-12-00009.1.
Lau, N.-C., 1988: Variability of the observed midlatitude storm tracks in relation to low-frequency changes in the circulation pattern. J. Atmos. Sci., 45, 2718–2743, https://doi.org/10.1175/1520-0469(1988)045<2718:VOTOMS>2.0.CO;2.
Lee, S., and I. M. Held, 1993: Baroclinic wave packets in models and observations. J. Atmos. Sci., 50, 1413–1428, https://doi.org/10.1175/1520-0469(1993)050<1413:BWPIMA>2.0.CO;2.
Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7A, 157–167, https://doi.org/10.3402/tellusa.v7i2.8796.
Lupo, A. R., 1997: A diagnosis of two blocking events that occurred simultaneously over the mid-latitude Northern Hemisphere. Mon. Wea. Rev., 125, 1801–1823, https://doi.org/10.1175/1520-0493(1997)125<1801:ADOTBE>2.0.CO;2.
Lupo, A. R., 2021: Atmospheric blocking events: A review. Ann. N. Y. Acad. Sci., 1504, 5–24, https://doi.org/10.1111/nyas.14557.
Ma, Q., V. Lembo, and C. L. E. Franzke, 2021: The Lorenz energy cycle: Trends and the impact of modes of climate variability. Tellus, 73A, 1900033, https://doi.org/10.1080/16000870.2021.1900033.
Nakamura, H., M. Nakamura, and J. L. Anderson, 1997: The role of high- and low-frequency dynamics in blocking formation. Mon. Wea. Rev., 125, 2074–2093, https://doi.org/10.1175/1520-0493(1997)125<2074:TROHAL>2.0.CO;2.
Oort, A. H., 1983: Global atmospheric circulation statistics, 1958–1973. NOAA Professional Paper 14, 180 pp.
Orlanski, I., 2003: Bifurcation in eddy life cycles: Implications for storm track variability. J. Atmos. Sci., 60, 993–1023, https://doi.org/10.1175/1520-0469(2003)60<993:BIELCI>2.0.CO;2.
Orlanski, I., 2005: A new look at the Pacific storm track variability: Sensitivity to tropical SSTs and to upstream seeding. J. Atmos. Sci., 62, 1367–1390, https://doi.org/10.1175/JAS3428.1.
Orlanski, I., and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 1972–1998, https://doi.org/10.1175/1520-0469(1991)048<1972:TLCOAC>2.0.CO;2.
Orlanski, I., and E. K. M. Chang, 1993: Ageostrophic geopotential fluxes in downstream and upstream development of baroclinic waves. J. Atmos. Sci., 50, 212–225, https://doi.org/10.1175/1520-0469(1993)050<0212:AGFIDA>2.0.CO;2.
Pan, Y., L. Li, X. Jiang, G. Li, W. Zhang, X. Wang, and A. P. Ingersoll, 2017: Earth’s changing global atmospheric energy cycle in response to climate change. Nat. Commun., 8, 14367, https://doi.org/10.1038/ncomms14367.
Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer, 710 pp.
Petterssen, S., and S. J. Smebye, 1971: On the development of extratropical cyclones. Quart. J. Roy. Meteor. Soc., 97, 457–482, https://doi.org/10.1002/qj.49709741407.
Randel, W. J., and J. L. Stanford, 1985: The observed life cycle of a baroclinic instability. J. Atmos. Sci., 42, 1364–1373, https://doi.org/10.1175/1520-0469(1985)042<1364:TOLCOA>2.0.CO;2.
Roebber, P. J., 1984: Statistical analysis and updated climatology of explosive cyclones. Mon. Wea. Rev., 112, 1577–1589, https://doi.org/10.1175/1520-0493(1984)112<1577:SAAUCO>2.0.CO;2.
Sanders, F., 1986: Explosive cyclogenesis in the west-central North Atlantic Ocean, 1981–84. Part I: Composite structure and mean behavior. Mon. Wea. Rev., 114, 1781–1794, https://doi.org/10.1175/1520-0493(1986)114<1781:ECITWC>2.0.CO;2.
Sanders, F., and J. R. Gyakum, 1980: Synoptic-dynamic climatology of the “bomb.” Mon. Wea. Rev., 108, 1589–1606, https://doi.org/10.1175/1520-0493(1980)108<1589:SDCOT>2.0.CO;2.
Schubert, S. D., and C.-K. Park, 1991: Low-frequency intraseasonal tropical–extratropical interactions. J. Atmos. Sci., 48, 629–650, https://doi.org/10.1175/1520-0469(1991)048<0629:LFITEI>2.0.CO;2.
Simmons, A. J., and B. J. Hoskins, 1978: The life cycle of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414–432, https://doi.org/10.1175/1520-0469(1978)035<0414:TLCOSN>2.0.CO;2.
Simmons, A. J., and B. J. Hoskins, 1980: Barotropic influence on the growth and decay of nonlinear baroclinic waves. J. Atmos. Sci., 37, 1679–1684, https://doi.org/10.1175/1520-0469(1980)037<1679:BIOTGA>2.0.CO;2.
Swanson, K., and R. T. Pierrehumbert, 1994: Nonlinear wave packet evolution on a baroclinically unstable jet. J. Atmos. Sci., 51, 384–396, https://doi.org/10.1175/1520-0469(1994)051<0384:DCCISF>2.0.CO;2.
Tanaka, S., K. Nishii, and H. Nakamura, 2016: Vertical structure and energetics of the western Pacific teleconnection pattern. J. Climate, 29, 6597–6616, https://doi.org/10.1175/JCLI-D-15-0549.1.
Thompson, D. W. J., B. R. Crow, and E. A. Barnes, 2017: Intraseasonal periodicity in the Southern Hemisphere circulation on regional spatial scales. J. Atmos. Sci., 74, 865–877, https://doi.org/10.1175/JAS-D-16-0094.1.
Ting, M., and N.-C. Lau, 1993: A diagnostic and modeling study of the monthly mean wintertime anomalies appearing in a 100-year GCM experiment. J. Atmos. Sci., 50, 2845–2867, https://doi.org/10.1175/1520-0469(1993)050<2845:ADAMSO>2.0.CO;2.
Tracton, M. S., 1990: Predictability and its relationship to scale interaction processes in blocking. Mon. Wea. Rev., 118, 1666–1695, https://doi.org/10.1175/1520-0493(1990)118<1666:PAIRTS>2.0.CO;2.
Tsou, C.-H., and P. J. Smith, 1990: The role of synoptic/planetary-scale interactions during the development of a blocking anticyclone. Tellus, 42A, 174–193, https://doi.org/10.3402/tellusa.v42i1.11869.
Xu, P., L. Wang, W. Chen, G. Chen, and I.-S. Kang, 2020: Intraseasonal variations of the British-Baikal corridor pattern. J. Climate, 33, 2183–2200, https://doi.org/10.1175/JCLI-D-19-0458.1.
Yang, W., J. Nie, P. Lin, and B. Tan, 2007: Baroclinic wave packets in an extended quasigeostrophic two-layer model. Geophys. Res. Lett., 34, L05822, https://doi.org/10.1029/2006GL029077.
Zhuge, A., and B. Tan, 2021: The springtime western Pacific pattern: Its formation and maintenance mechanisms and climate impacts. J. Climate, 34, 4913–4936, https://doi.org/10.1175/JCLI-D-20-0051.1.
